Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
138 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C4⋊#14556681 | C2 | semidirect |
| 2. C4×#14556681 | C2 | semidirect |
| 39. D4×C73 | C32 | semidirect |
| 68. C73 | D4⋊C32 | semidirect |
| 104. D4 | #14556681 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊#14556681 | 2 |
| C4×#14556681 | 2 |
| D4×#11924031 | 2 |
| D4⋊C32 | 73 |